The Effect of Interconnecting Ribbons in External Resistance of Crystalline Silicon Photovoltaic Modules

The interconnecting ribbons in commercial crystalline silicon (c-Si) photovoltaic (PV) modules significantly contribute to the external resistance of the modules. This external resistance plays a major role in resistive losses in the modules and thus measures should be taken in minimization of such resistances. A wider ribbon cause blockage for the incoming light in the solar cells. In addition, the selection of wrong ribbon configuration essentially leads to breakage in fingers which further enhances resistive losses in the modules. In this paper, an analytical approach using a resistive network model has been proposed which effectively describes the effect of ribbon dimension on the blockage area as well as external resistance of the modules. The model has been useful to understand the resistive effect in the PV modules in a quantitative manner. The results show that the number of busbars and the width of the busbars in a solar cell play a significant role in choosing the right ribbon configuration. The proposed approach is useful to understand the optimum ribbon configuration in newly manufactured c-Si PV modules.


Introduction
Solar photovoltaic (PV) is one of the fastest growing technologies for clean and renewable electricity generation.In this technology, crystalline silicon (c-Si) is the most widely used material that has the highest share of deployment across the world [1][2][3].PV modules are the commercially available components for production of electricity [4][5][6].In such commercial crystalline silicon PV modules, the smallest power generating unit are the individual solar cells; those are connected by means of electrical interconnections, termed as interconnecting ribbons [7][8][9].These ribbons play a vital role in determining the net series resistance of the module.The series resistance leads to power dissipation in the modules, which in turn generates additional heat that reduces the overall module performance.Since the modules are further connected in the form of solar array, the effect escalates in such a larger scale.That may also lead to mismatch and the overall performance of the entire PV system degrades [10][11][12].Therefore, the study on the effect of the interconnecting ribbons on the series resistance of the modules is crucial.
In PV modules, the interconnecting network of the ribbons (including junction box) creates additional series resistance in the modules, which is often termed as the external resistance [13].Typically, the interconnecting ribbons are attached to the busbars of one solar cell at the top to the bottom of the adjoined cell [14,15].However, poor ribbon configurations may induce both shadowing and resistive losses and consequently lead to performance degradation in PV modules [16].Also, any deviation in the solder configuration of interconnecting ribbons cause breakage in fingers which accelerates the increase in series resistance of the module.It is evident from the literature that one of the major causes of finger breakage is the interconnecting ribbons i.e., the expansion and contraction of which facilitates crack in fingers and hence, finger breakage [17][18][19].It has also been observed that the finger breakage can occur only at that side of the busbar where the interconnecting ribbons are in contiguity with the fingers, which may occur either due to use of a wider ribbon or poor placement of the ribbons [17].Therefore, it is essential to understand the effect of ribbon width and the placement of ribbons on top of the busbars in the solar cells.This paper addresses about the effect of such interconnecting ribbons on the series resistance of the PV modules and ways to mitigate such effects.By an analytical circuit network and a numerical approach, the effects of interconnecting ribbons on the external resistance of the modules due to varying ribbon width has been exploited.Ways to minimize the external resistance and the overall series resistance of the PV system has also been discussed.

Relation between excess width and area blocked by the interconnecting ribbon
The width of the interconnecting ribbons plays a key role in the resistive losses in the PV modules.However, apart from the resistive losses an insight into the ribbon width with other associated losses should be considered.As the width of the ribbon exceeds the width of the busbar in a solar cell, it creates additional shadowing effect i.e., the excess width blocks the incoming light rays falling on the solar cell.Taking width of the ribbon,   ; length of the ribbon,   at the front side of the solar cell; width of busbar,   and number of busbars in a cell,   , the excess ribbon width which blocks the light can be obtained as, Further, the net excess ribbon area associated with the blockage of cell area in a single solar cell can be obtained as, Furthermore, the relative cell area blocked in a solar cell due to excess ribbon width can be expressed as, Where   the area of the solar cell.The relative blockage in cell area due to the excess ribbon width has been studied in a numerical approach.For different extent of excess ribbon width, the corresponding relative blockage in cell area (%) has been plotted in Figure 1.Since the busbar width varies on manufacturer basis, a lower value of the same has been considered [20].Since the number of busbars also varies on manufacturer basis, up to five numbers of busbars has been considered for the plot.From the figure, it is evident that more the number of busbars more is the blockage area due to excess ribbon width.In addition, for higher number of busbars, the inclination in the slope suggests that the blockage area escalates and nearly 5% of the cell area could be blocked for an excessive ribbon width, which is significant loss in the incoming light to the solar cell.The blockage area, hence the loss would escalate further for multiple cells in the module and furthermore in the array scale.Therefore, by choosing a narrow ribbon width, this loss can be eliminated.It would also help in minimizing the finger breakages under field operations.However, choosing a narrow ribbon would result in an increased external resistance hence increased resistive losses.Therefore, the resistive loss due to the varying ribbon width is studied further.

Calculation of external resistance due to interconnecting ribbons
The net series resistance of the module is constituent of the individual resistance of the solar cells, and also the external resistance due to the interconnecting ribbons along with other residual resistances.As the external resistance and the power loss are interrelated, a limited increase in the external resistance will add up to the excess power loss in the module.Collectively, the effect would escalate in array scale.
That is why it is essential to understand the impact of the change in external resistance due to change in the ribbon dimension.Typically, the height of the ribbon is limited to a standard extent as to generate less stress while packing different module layers.However, the width of the ribbon is the key, the effect of which on the external resistance is studied further.
To serve this purpose, an equivalent circuit diagram containing all the components of the external resistances in a commercial crystalline silicon PV module is shown in Figure 2. It has been assumed that all the cells are connected in series, which is the case in most of the commercial modules.Individual solar cell resistances have not been considered as that depends entirely on the type, grade, and processing of the individual cell manufacturers, which is beyond the scope of this paper.The circuit diagram comprises of the outer terminal resistances at the junction box, termed as  1 and  2 respectively for positive and negative side of the terminals; the contact resistances of the interconnecting ribbons with the front and back of the solar cells, termed as   and   respectively; the bulk ribbon resistance on the top of the solar cell, termed as  1 ; the bulk ribbon resistance in between two solar cells, termed as  2 , and the residual resistances between the interconnecting strings in the module, termed as  3 .
Using these resistive components, the net external resistance of the module can be formulated as, Where   is the number of cells;   is the number of busbars in a cell and   is the number of strings in the module.The resistance of the residual resistances between the interconnecting strings and that of the outer terminals have no such major impact on the finger breakages, and in dimensional point of view, it varies from manufacturer to manufacturer.Therefore, it has been regarded as an additional resistance (  ) and for the calculations, a standard resistance value of the same has been considered.Now, the net external resistance of the module can be represented as,   = (  +  1 +   ) + (  − 1) 2 +   (5) Where, The ribbons create metallic contacts with the front and back side of the solar cells.The contact resistances   and   can be formulated as,   =    and   =    (7) Where  is the specific contact resistance for metal-to-metal contacts;   and   are the contact area of the ribbons at the front and back of the solar cells respectively.Now the interconnecting ribbons runs over the busbars in the solar cells.For the case where the ribbon width is less than that of the busbar, the contact area of the ribbon on top of the busbars can simply be expressed as       and if the busbar width is less than the ribbon width, the same can be expressed as       .However, in the latter case the additional contact area of ribbons with the area adjacent to the busbars need to be considered as well.The area of interest here is only the metal-to-metal contact, since it possesses the least series resistance.The part of the ribbon that touches the top ARC layer of the cell practically conducts little to negligible current, therefore it has not been considered.Rather, the excess ribbon width which gets in contact with the metallic fingers underneath it; is the region of interest.Now, the fingers are typically placed in contact with the busbars in a perpendicular connection.Therefore, the contact area for the excess part of the ribbon on the top of the fingers can be written as (  −   )      , where   is the width of the finger and   is the number of fingers underneath the excess part of the ribbon.
Therefore, the net effective contact area of interconnecting ribbons in a single solar cell at the front side of the cell, considering metallic contact is,   =       , for   <   =       + (  −   )      , for   >   (8) Similarly, the contact area of the ribbons at the back side of the solar cell can be represented as, Where,   is the length of the ribbon at the back side of the solar cell.Now in order to obtain the bulk resistance (  ) of the ribbon, it is essential to know the material composition of the ribbons.For standard, the ribbons are made from copper, with a surrounding tin coating [17].Considering this configuration, the bulk ribbon resistance can be expressed as,   =           +    (10) Where,   is the length of ribbon,   and   are the resistivity of copper and tin respectively;   and   are the cross-sectional area of copper and tin in the ribbons.

Results and Discussion
The external resistances of a module for varying ribbon width and for different number of busbars have been calculated numerically using equation ( 5) and plotted graphically in Figure 3.Some constituent parameters have been obtained from a commercial c-Si module having two strings and cell size of 15.6 cm 2 , and some has been taken from the standard values.It is evident from the graph that the external resistance declined rapidly on raising the ribbon width.However, the external resistance does not vary much under this variation.Therefore, by choosing a ribbon narrower than the busbar width could effectively eliminate the shadowing effect as well as it would be preventive in breakage of fingers during field operations.Furthermore, it is also observed from the graph that for lesser number of busbars, there is a sharp declination in the external resistance while there is hardly any change for higher number of busbars.Therefore, by choosing solar cells having higher number of busbars, the net external resistance due to interconnecting ribbons could be minimized.

Conclusion
An analytical approach has been presented to understand the effect of interconnecting ribbons on the series resistance of commercial crystalline silicon PV modules.By means of numerical approach, it has been observed that the shadowing effect of excess ribbon width is significant and the effect escalates with increasing number of busbars in the solar cells.An equivalent circuit model of the interconnecting ribbon network in the commercial modules has been presented, that can be useful to understand the effect of different resistance components involved in such a network.The effect of varying ribbon width in the external resistance, hence the series resistance of the module with increasing number of busbars has been observed.It has been understood that by choosing a lower width of interconnecting ribbon (less than that of busbars) both the shadowing effect as well as finger breakages can be minimized, which in turn will help in minimizing the series resistance.Though, it would result in an increase in the external resistance as compared to that in the case of wider ribbons.However, with the increasing number of busbars in the cells, the effective external resistance, hence the series resistance can be minimized.

Figure 1 .
Figure 1.Plot between blocked area (%) and excess width of the interconnecting ribbons for different number of busbars in a solar cell.

Figure 2 .
Figure 2. Equivalent circuit diagram for external resistance network in a PV module with varying number of busbars.

Figure 3 .
Figure 3. External series resistance of a PV module for varying ribbon width and for different number of busbars.